..type tremelos aren't unusual on Ibanezes or most "metal" style guitars, just beware of very CHEAP floyds/guitars with floyds as,from my experience they are fuggging awful.
Note this does not usually apply to a well maintained Ibanez floyd - just make sure you tell them in the shop to set the whole thing how YOU like it (string height wise mainly), dont let the sales suit pressure you. If you want it lower (within reason!) just ask them nicely, read the instructions and don't adjust it yourself UNTIL you are 200% sure of what you are doing :) Some shops offer a first year service so you may want to find one that does that.
Floyds can be vexatious as they can lock at both ends (nut and tremelo) and you must make sure the new strings are stretched enough to hold their tune before you lock the nut..etc,etc.
i usually only deal with older style trems and don't have
much experience of these, but they are apparently good on Ibinbads, ESPs etc... with a few exceptions.
Accuracy,you say? hmm interesting concept..